In topology, a formal ball is an extension of the notion of ball to allow unbounded and negative radius. The concept of formal ball was introduced by Weihrauch and Schreiber in 1981 and the negative radius case (the generalized formal ball) by Tsuiki and Hattori in 2008.
Specifically, if
Formal balls possess a partial order
Generalized formal balls are interesting because this partial order works just as well for
Formal balls possess the Lawson topology and the Martin topology.